Find whether the following functions are even or odd or none `f(x) = log(x+sqrt(1+x^2))`

Determine whether the following functions are even or odd. {:((i)f(x)=log(x+sqrt(1+x^(2))),(ii)f(x)=x((a^(x)+1)/(a^(x)-1))),((iii)f(x)=sinx+cosx,(iv)f(x)=x^(2)-abs(x)),((v)f(x)=log((1-x)/(1+x)),(vi)f(x)={(sgn x)^(sgnx)}^(n)," n is an odd integer"):} {:((vii) f(x)=sgn(x)+x^(2),""),((viii)f(x+y)+f(x-y)=2f(x)*f(y)," where " f(0) ne 0 and x","y ne R.,""):}

Determine whether the following functions are even or odd or neither even nor odd: f(x)=(x^(2)-1)|x|

Determine whether the following functions are even or odd or neither even nor odd: sin(x^(2)+1)

Find whether the following functions are one-one or many-one f(x)=sqrt(1-e^(1/x-1))

Determine whether the following function are even/odd/neither even nor odd? f(x)=xlog(x+sqrt(x^(2)+1))

Determine whether the following functions are even or odd or neither even nor odd: x+x^(2)

Find whether the following function is even or odd: f(x) = x tan^3x + x^(3)"cosec" x

Determine whether the following functions are even or odd or neither even nor odd: f(x)=x((a^(x)-1)/(a^(x)+1))

Determine whether the following functions are even or odd or neither even nor odd: f(x)=sinx+cosx

Which of the following functions is (are) even, odd or neither: f(x)=log((1-x)/(1+x))